The answer to the classic part of the puzzle is that because the man's neighbour is snoring he telephones him to wake him up and thus stops him from snoring.
The explanation for my variant is that once the man has stopped his neighbour from snoring he lies ON THE BROAD OF HIS BACK so that he will deliberately begin snoring. This is to revenge himself on his neighbour but because he has taken the phone off the hook his neighbour can't wake him up.